With the advent and rapid growth of massive open online courses (MOOCs) in the world education market in the last decade, online learning technologies are becoming increasingly widespread not only in the non-formal education sector but also in higher and supplementary vocational education. The use of MOOCs for implementing educational programs at the universities opens wide opportunities in terms of expanding the educational choice of students, the development of virtual academic mobility, reducing the cost of educational services, and improving the accessibility of education. However, the effectiveness of using different online learning technologies in the educational process of universities and the consequences of their widespread adoption has not been sufficiently explored.In this research a comparative analysis based on an empirical study of the application of different online-learning models in the educational process within a university was carried out. An experiment was undertaken in which different groups of students of the Ural Federal University were encouraged to master some disciplines in the framework of a blended learning model and an online learning model with tutoring support. The results of the pilot study were compared with the training results of a control group of students who mastered the same disciplines in a traditional taught format. It was shown that both models using MOOCs in the educational process demonstrated greater effectiveness in comparison with the traditional model; both in terms of educational outcomes of students and in terms of their satisfaction with the learning process. For engineering and technical disciplines, there is no statistically significant difference in using blended or online learning technologies, whereas for humanitarian disciplines, where the communicative component of the learning process is significant, the blended learning technology produced better results. Conclusions of the empirical research can be useful for heads of educational organizations and teachers in the modernization of the educational process, improving teaching methods, and increasing the effectiveness of new educational technologies. The results of the research will also be used for implementing the State Priority Project "The Modern Digital Educational Environment of the Russian Federation".

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We study magnetoelastic resonance phenomena in a mono-axial chiral helimagnet belonging to hexagonal crystal class. By computing the spectrum of coupled elastic wave and spin wave, it is demonstrated how hybridization occurs depending on their chirality. Specific features of the magnetoelastic resonance are discussed for the conical phase and the soliton lattice phase stabilized in the mono-axial chiral helimagnet. The former phase exhibits appreciable non-reciprocity of the spectrum, the latter is characterized by a multi-resonance behavior. We propose that the nonreciprocal spin wave around the forced-ferromagnetic state has potential capability to convert the linearly polarized elastic wave to circularly polarized one with the chirality opposite to the spin wave chirality.

Relevance. The worldwide spread of a new infection SARS-CoV-2 makes relevant the analysis of the socio-economic factors that make modern civilization vulnerable to previously unknown diseases. In this regard, the development of mathematical models describing the spread of pandemics like COVID-19 and the identification of socio-economic factors affecting the epidemiological situation in regions is an important research task. Research objective. This study seeks to develop a mathematical model describing the spread of COVID-19, thus enabling the analysis of the main characteristics of the spread of the disease and assessment of the impact of various socio-economic factors. Data and methods. The study relies on the official statistical data on the pandemic presented on coronavirus sites in Russia and other countries, Yandex DataLens dataset service, as well as data from the Federal State Statistics Service. The data were analyzed by using a correlation analysis of COVID-19 incidence parameters and socio-economic characteristics of regions; multivariate regression – to determine the parameters of the probabilistic mathematical model of the spread of the pandemic proposed by the authors; clustering – to group the regions with similar incidence characteristics and exclude the regions with abnormal parameters from the analysis. Results. A mathematical model of the spread of the COVID-19 pandemic is proposed. The parameters of this model are determined on the basis of official statistics on morbidity, in particular the frequency (probability) of infections, the reliability of the disease detection, the probability density of the disease duration, and its average value. Based on the specificity of COVID-19, Russia regions are clustered according to disease-related characteristics. For clusters that include regions with typical disease-related characteristics, a correlation analysis of the relationship between the number of cases and the rate of infection ( with the socio-economic characteristics of the region is carried out. The most significant factors associated with the parameters of the pandemic are identified. Conclusions. The proposed mathematical model of the pandemic and the established correlations between the parameters of the epidemiological situation and the socio-economic characteristics of the regions can be used to make informed decisions regarding the key risk factors and their impact on the course of the pandemic.

This article describes a probabilistic mathematical model which can be used to analyse traffic flows in a road network. This model allows us to calculate the probability of distribution of vehicles in a regional road network or an urban street network. In the model, the movement of cars is treated as a Markov process. This makes it possible to formulate an equation determining the probability of finding cars at key points of the road network such as street intersections, parking lots or other places where cars concentrate. For a regional road network, we can use cities as such key points. This model enables us, for instance, to use the analogues of Kirchhoff First Law (Ohm's Law) for calculation of traffic flows. This calculation is based on the similarity of a real road network and resistance in an electrical circuit. The traffic flow is an analogue of the electric current, the resistance of the section between the control points is the time required to move from one key point to another, and the voltage is the difference in the number of cars at these points. In this case, well-known methods for calculating complex electrical circuits can be used to calculate traffic flows in a real road network. The proposed model was used to calculate the critical load for a road network and compare road networks in various regions of the Ural Federal District.